English

Convergence from below suffices

Functional Analysis 2014-12-25 v1

Abstract

An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in any introductory course on measure and integration.

Keywords

Cite

@article{arxiv.1412.7702,
  title  = {Convergence from below suffices},
  author = {J. F. Feinstein},
  journal= {arXiv preprint arXiv:1412.7702},
  year   = {2014}
}

Comments

5 pages, no figures

R2 v1 2026-06-22T07:43:23.248Z